Apparently I need "Static DHCP" to be able to do this. Both Tomato and dd-rwt are viable options in this tutorial. After going to polarcloud.com I discovered my router (a Linksys E1000) was too new to support Tomato. That's when I found Tomato USB which supported the Linksys E1000, but hasn't been updated since 2010. The Tomato USB website links here to this thread: http://www.linksysinfo.org/index.php?threads/tomato-modifications.26037/ with a list of Tomato mods.

So I'm left with deciding which Tomato mod to choose and yet I have no clue. All I need from it is to be reliable and have Static DHCP.